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附錄 A 循環回收法原始公式推導 F d (1-α) MP F (1-d) (1-α) R rt α W A S T E P rv 附圖 A.1 循環回收生命週期圖 (Vellini and Savioli, 2009) F: 回收再製率 ; d: waste,%; α: 重複使用率 MP F(1-d) P R Fd 1-F W A S T E 1.P 圖 B.2 循環回收生命週期圖 (P R 觀點 ) 廢棄 : (1-F) + Fd 使用 : F(1-d) E[n P ] = 使用次數 * 廢棄量 = 1*{(1-F) + Fd } +2*{ F(1-d)[ (1-F) + Fd]} +3*{ F^2(1-d)^2[ (1-F) + 91
Fd]} + = n=0 n [1 F(1 d)] [F(1 d)] n 1 = [1-F(1-d)] n=0 n [F(1 d)] n 1 = 1 1 F(1 d) 2.R 廢棄 : Fd+F(1-d)*(1-F) 使用 : F(1-d) E[nR]= 使用次數 * 廢棄量 = 1*[F(1-d)(1-F)+Fd] +2*[F^2(1-d)^2(1-F)+F^2(1-d)d] +3*[F^3(1-d)^3(1-F)+F^3(1-d)^2d] + = n=0 [F n (1 d) n (1 F) + F n (1 d) n 1 d] = [1-F(1-d)]*F* n=0 [F(1 d)] n 1 = F [1 F(1 d)] rt α P rv 1-α 1.E[n rv ]= E[n^rV]*E[n P ] 針對 rv 而 廢棄 : (1 α) 使用 : α 圖 B.3 循環回收生命週期圖 (rv rt 觀點 ) E[n^rV]= 1(1 α) + 2α(1 α) +3α 2 (1 α) + = (1-α) n=0 n α n 1 92
E[n rv ]= = 1 1 α 1 (1 α)[1 F(1 d)] 2.E[n rt ]= E[n^rT]*E[n P ] 針對 rt 而言 廢棄 : α(1 α) 使用 : α E[n^rT]= 1α(1 α) + 2α 2 (1 α) +3α 3 (1 α) + = (1-α) n=0 n α n = E[n rt ]= α 1 α α (1 α)[1 F(1 d)] 93